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Differential Equations

Course name: Differential Equations
Course number: XYZ
Knowledge area: Math

Administrative details

Faculty: Computer Science and Engineering
Year of instruction: 2nd year of BS
Semester of instruction: 1st semester
No. of Credits: 4 ECTS
Total workload on average: 144 hours overall
Class lecture hours: 2 per week
Class tutorial hours: 2 per week
Lab hours: 2 per week
Individual lab hours: 0
Frequency: weekly throughout the semester
Grading mode: letters: A, B, C, D

Prerequisites

Mathematical Analysis I
Mathematical Analysis II
Analytic Geometry and Linear Algebra I
Analytic Geometry and Linear Algebra II

Course outline

The course is designed to provide Software Engineers and Computer Scientists by knowledge of basic (core) concepts, definitions, theoretical results and techniques of ordinary differential equations theory, basics of power series and numeric methods, applications of the all above in sciences. All definitions and theorem statements (that will be given in lectures and that are needed to explain the keywords listed above) will be formal, but just few of these theorems will be proven formally. Instead (in the tutorial and practice classes) we will try these definitions and theorems on work with routine exercises and applied problems. The course is based on a textbook “Elementary Differential Equations” by William F. Trench (2001).

Expected learning outcomes

The course will provide an opportunity for participants to:

know mathematical theory of linear ordinary differential equations, elements of basic numeric methods;
understand application value of ordinary differential equations, functional series, and numeric methods;
get practical (pen-and-paper as well as computer-aided) experience with solving ordinary differential equations and using them for modelling in Science.

Programming related learning outcomes

Course includes computational practice assignment that assumes implementation of three numeric methods,namely:

Euler method,
improved Euler method,
Runge-Kutta method.

Special attention will be paid for the quality and the OO-style of the implementation.

Expected acquired core competences

Ordinary differential equations (ODE),
initial value problems;
linear, first, second and higher-order ODE’s;
separable and exact ODE’s; order reduction;
power and Fourier series;
Newton method for algebraic equations;
Euler and Runge-Kutta methods for ODE’s;
Laplace transform;
partial differential equations.

Textbook

Reference material

Required computer resources

Students should have laptops with any programming language installed (while Java is preferred).

Evaluation

Grading items:
- In-class participation 1 point per week for each individual contribution in class (i.e. 14 points overall).
- Final overall in-course participation/contribution (“instructors’ gratitude”) 6 points.
- Each in-class theory or practice tests – up to 10 points (i.e. 40 points overall).
- Mid-term exam up to 40 points, final examination up to 40 points (i.e. 80 points overall).
- computational practice assignment up to 10 points for each task (i.e. up to 30 points for 3 tasks),
Final grade scale:
- A: 136..170 points (i.e. 80% at least);
- B: 102..135 points (i.e. 60% at least);
- C: 68..101 points (i.e. 40% at least);
- D: less than 68 points.

BSc:DifferentialEquations old

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